Some Analytical Solitary Wave Solutions for the Generalized q-Deformed Sinh-Gordon Equation: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mo>∂</mml:mo></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mi>θ</mml:mi></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mo>∂</mml:mo><mml:mi>z</mml:mi><mml:mo>∂</mml:mo><mml:mi>ξ</mml:mi></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mi>α</mml:mi><mml:msup><mml:mrow><mml:m

Eleuch, Hichem

doi:10.1155/2018/5242757

Cited by 22 publications

(1 citation statement)

References 76 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another type of potential function commonly used to effects of shifts and asymmetry in the medium under investigation is the q-deformed potentials [58,59]. Various analytical solutions of the nonlinear systems with q-deformed potential are present in the literature [58,59], however the majority of the solutions are valid for models other than fNLSE and valid for steady-state conditions. In order to investigate the effects of q-deformation on the solitons of the fNLSE, we use a q-deformed Rosen-Morse potential.…”

Section: Resultsmentioning

confidence: 99%

Petviashvili Method for the Fractional Schrödinger Equation

Bayındır¹,

Farazande²

2021

Preprint

View full text Add to dashboard Cite

In this paper, we extend the Petviashvili method (PM) to the fractional nonlinear Schrödinger equation (fNLSE) for the construction and analysis of its soliton solutions. We also investigate the temporal dynamics and stabilities of the soliton solutions of the fNLSE by implementing a spectral method, in which the fractional-order spectral derivatives are computed using FFT routines, and the time integration is performed by a 4 th order Runge-Kutta time-stepping algorithm. We discuss the effects of the order of the fractional derivative, α, on the properties, shapes, and temporal dynamics of the solitons solutions of the fNLSE. We also examine the interaction of those soliton solutions with zero, photorefractive and q-deformed Rosen-Morse potentials. We show that for all of these potentials the soliton solutions of the fNLSE exhibit a splitting and spreading behavior, yet their dynamics can be altered by the different forms of the potentials considered. The splitting and spreading dynamics of the solitons of the fNLSE are not affected by noise. Our results also indicate that the Savitzky-Golay filter can be used for the denoising of the solitons of the fNLSE.

show abstract

Section: Resultsmentioning

confidence: 99%

Petviashvili Method for the Fractional Schrödinger Equation

Bayındır¹,

Farazande²

2021

Preprint

View full text Add to dashboard Cite

show abstract

Investigating new solutions for a general form of q$$ \mathfrak{q} $$‐deformed equation: An analytical and numerical study

Ali,

Mohamed,

Alharbi

2024

Circuit Theory & Apps

View full text Add to dashboard Cite

SummaryThis paper contributes to the study of a new model called the ‐deformed equation or the ‐deformed tanh‐Gordon model. To understand physical systems with violated symmetries. We utilize the ‐expansion approach to solve the ‐deformed equation for specific parameter values. This method generates solutions that provide valuable insights into the system's dynamics and behavior. To verify the accuracy of our solutions, we also apply the finite difference technique to obtain numerical solutions to the ‐deformed equation. This dual approach ensures the reliability of our results. We present our findings using tables and graphics to enhance clarity and facilitate comparison between the analytical and numerical solutions. These visual aids help readers better understand the similarities and differences between the two approaches. The ‐deformation is significant as it models physical systems with nonstandard symmetry features, like extensivity, offering a more accurate representation of real‐world phenomena. The growing significance of this equation across various disciplines highlights its potential in advancing our understanding of complex physical systems. This paper contributes valuable knowledge about the ‐deformed equation, demonstrating its potential for accurately modeling physical systems with violated symmetries. Through both analytical and numerical techniques, we offer comprehensive solutions and validate their accuracy, with graphical representations enhancing the clarity and understanding of our results. This exploration of ‐deformation advances modeling techniques, providing a more precise depiction of real‐world processes with nonstandard symmetry features.

show abstract

Further physical study about solution structures for nonlinear q-deformed Sinh–Gordon equation along with bifurcation and chaotic behaviors

Bai,

Qi,

Sun

2023

Nonlinear Dyn

View full text Add to dashboard Cite

In this article, with the help of Matlab R2021a software, the exact solutions of the nonlinear q-deformed Sinh-Gordon equation are successfully examined by ( G ′ G 2 )expansion method. The main novelty of this paper lies in five aspects: (1) To our best knowledge, the modified ( G ′ G 2 )expansion method was firstly applied in nonlinear q-deformed Sinh-Gordon equation (NQSGE). And thus get many new solutions that were not found previously literature [51,49].(2) The effects of wave obliqueness about NQSGE are firstly discussed in this paper which did not happen in previous papers [44,45,49,51,40]. (3) Phase portraits and bifurcation behaviors about NQSGE are also firstly investigated in Hamiltonian system that did not appear in previous literatures [44,45,49,51,40]. (4) Sensitive analysis to initial value and chaotic behavior are also firstly studied in NQSGE. This is also a work not done in other previous literatures [44,45,49,51,40]. (5) The modified Riemann-Liouville, Beta, Conformable and M-truncated fractional derivatives are tested for accuracy in Fig. 18 (a) and (b). To our best knowledge, we seem firstly compare the relations and distinctions among different fractional order derivatives in NQSGE model. The generalizations (1)-( 5) indicated the wave propagation of solitions about NQSGE model is mastered by the changed fraction, changed wave obliqueness angle and other

show abstract

Some Analytical Solitary Wave Solutions for the Generalized q-Deformed Sinh-Gordon Equation: ∂2θ/∂z∂ξ=α

Abstract: We introduce the generalized q-deformed Sinh-Gordon equation and derive analytical soliton solutions for some sets of parameters. This new defined equation could be useful for modeling physical systems with violated symmetries.

Cited by 22 publications

References 76 publications

Petviashvili Method for the Fractional Schrödinger Equation

Petviashvili Method for the Fractional Schrödinger Equation

Investigating new solutions for a general form of q$$ \mathfrak{q} $$‐deformed equation: An analytical and numerical study

Further physical study about solution structures for nonlinear q-deformed Sinh–Gordon equation along with bifurcation and chaotic behaviors

Contact Info

Product

Resources

About